Question 3

An old tanker is $$100$$ km due north of a cruise liner. The tanker sails Southeast at a speed of $$20$$ kilometers per hour and the liner sails Northwest at a speed of $$10$$ kilometres per hour. What is the shortest distance between the two boats during the subsequent motion?

Solution

The two boats move along parallel lines in opposite directions, with relative speed $$30$$ kilometers per hour. The initial separation is perpendicular to their common direction of motion, so the minimum distance is obtained by resolving the initial separation onto the perpendicular direction. This gives $$100\cos45^\circ=50\sqrt{2}$$ km.

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An old tanker is $$100$$ km due north of a cruise liner. The tanker sails Southeast at a speed of $$20$$ kilometers per hour and the liner sails Northwest at a speed of $$10$$ kilometres per hour. What is the shortest distance between the two boats during the subsequent motion?

Solution

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